Assuming that the user isn't part of the group portion of the folder and thus able to have access via permissions set for the group (if the group has execute and read access), no. Usually, when users attempt to gain access to directories (folders) they will simply be told "Permission denied".
AFAIK. I don't think I've ever seen a situation in *nix where it asks for a password to a directory when you don't have permission.
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